A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910019160637440 |
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| author | Müller-Hoissen, Folkert Ye, Rusuo |
| author_facet | Müller-Hoissen, Folkert Ye, Rusuo |
| contents | Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup-Newell hierarchy. A reduction from the latter system to an integrable matrix version of the Fokas-Lenells equation is then shown to inherit a corresponding vectorial Darboux transformation. Matrix soliton solutions are derived from the trivial seed solution. Furthermore, the Darboux transformation is exploited to determine in a systematic way exact solutions of the two-component vector Fokas-Lenells equation on a plane wave background. This comprises breathers, dark solitons, rogue waves and "beating solitons". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation Müller-Hoissen, Folkert Ye, Rusuo Exactly Solvable and Integrable Systems Mathematical Physics 37K10, 35C08, 35Qxx Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup-Newell hierarchy. A reduction from the latter system to an integrable matrix version of the Fokas-Lenells equation is then shown to inherit a corresponding vectorial Darboux transformation. Matrix soliton solutions are derived from the trivial seed solution. Furthermore, the Darboux transformation is exploited to determine in a systematic way exact solutions of the two-component vector Fokas-Lenells equation on a plane wave background. This comprises breathers, dark solitons, rogue waves and "beating solitons". |
| title | A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 37K10, 35C08, 35Qxx |
| url | https://arxiv.org/abs/2508.17534 |